Subgroups — C₂×C₆₇×#3021 #30739636

Order 17152.

4934 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#535×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3021	C₂	1	16	yes	maximal, direct product factor
5	C₂×#454×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#453×C₆₇	C₂	1	4	yes	maximal, complemented
7	C₂×#421×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#413×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#585×C₆₇	—	2	4	no	—
10	#585×C₆₇	—	2	8	no	—
11	#585×C₆₇	C₂²	1	8	yes	complemented
12	C₂×2₋¹⁺⁴×C₆₇	—	2	2	no	—
13	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
14	C₂×H(5,𝔽₂)×C₆₇	—	2	2	no	—
15	C₂×H(5,𝔽₂)×C₆₇	—	2	2	no	—
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
17	C₂²×#41×C₆₇	—	2	4	no	—
18	C₂²×#41×C₆₇	—	2	2	no	—
19	C₂²×#41×C₆₇	C₂²	1	2	yes	—
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
23	C₂×AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	8	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	16	yes	complemented
26	C₂²×SD₁₆×C₆₇	—	2	2	no	—
27	C₂²×D₈×C₆₇	—	2	2	no	—
28	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
29	#535×C₆₇	—	2	4	no	—
30	#535×C₆₇	C₂²	1	8	yes	complemented
31	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
32	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#121×C₆₇	—	2	2	no	—
34	C₂×#120×C₆₇	—	2	2	no	—
35	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#454×C₆₇	C₂²	1	32	yes	complemented
37	#453×C₆₇	C₂²	1	32	yes	complemented
38	#421×C₆₇	C₂²	1	16	yes	complemented
39	C₂×#104×C₆₇	C₂²	1	8	yes	complemented
40	#413×C₆₇	C₂²	1	8	yes	complemented
41	C₂×#101×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#100×C₆₇	C₂²	1	2	yes	complemented
43	C₂⁵×C₆₇	—	2	1	no	—
44	2₋¹⁺⁴×C₆₇	—	2	16	no	—
45	2₋¹⁺⁴×C₆₇	—	2	8	no	—
46	2₋¹⁺⁴×C₆₇	—	2	4	no	—
47	2₋¹⁺⁴×C₆₇	—	2	16	no	—
48	2₋¹⁺⁴×C₆₇	C₂³	1	8	yes	complemented
49	H(5,𝔽₂)×C₆₇	—	2	16	no	—
50	H(5,𝔽₂)×C₆₇	—	2	16	no	—
51	H(5,𝔽₂)×C₆₇	—	2	8	no	—
52	H(5,𝔽₂)×C₆₇	—	2	16	no	—
53	H(5,𝔽₂)×C₆₇	—	2	4	no	—
54	H(5,𝔽₂)×C₆₇	—	2	16	no	—
55	H(5,𝔽₂)×C₆₇	C₂³	1	8	yes	complemented
56	C₂×#41×C₆₇	—	2	4	no	—
57	C₂×#41×C₆₇	—	2	8	no	—
58	C₂×#41×C₆₇	—	2	4	no	—
59	C₂×#41×C₆₇	—	2	32	no	—
60	C₂×#41×C₆₇	—	2	16	no	—
61	C₂×#41×C₆₇	—	2	32	no	—
62	C₂×#41×C₆₇	—	2	4	no	—
63	C₂×#41×C₆₇	—	2	4	no	—
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	2	4	no	—
67	C₂×#41×C₆₇	—	2	16	no	—
68	C₂×#41×C₆₇	—	2	2	no	—
69	C₂×#41×C₆₇	—	2	2	no	—
70	C₂×#41×C₆₇	—	2	4	no	—
71	C₂×#41×C₆₇	—	2	4	no	—
72	C₂×#41×C₆₇	—	2	4	no	—
73	C₂×#41×C₆₇	D₄	1	4	yes	—
74	C₂×#41×C₆₇	D₄	1	4	yes	complemented
75	C₂×#41×C₆₇	D₄	1	8	yes	complemented
76	C₂×#41×C₆₇	C₂³	1	4	yes	—
77	C₂×#41×C₆₇	C₂³	1	8	yes	—
78	C₂×#41×C₆₇	C₂³	1	4	yes	—
79	C₂²×Q₈×C₆₇	—	2	2	no	—
80	C₂²×Q₈×C₆₇	—	2	4	no	—
81	C₂²×Q₈×C₆₇	D₄	1	2	yes	complemented
82	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₆₇	—	2	8	no	—
84	C₂²×D₄×C₆₇	—	2	2	no	—
85	C₂²×D₄×C₆₇	—	2	4	no	—
86	C₂²×D₄×C₆₇	—	2	2	no	—
87	C₂²×D₄×C₆₇	—	2	4	no	—
88	C₂²×D₄×C₆₇	—	2	4	no	—
89	C₂²×D₄×C₆₇	—	2	2	no	—
90	C₂²×D₄×C₆₇	—	2	2	no	—
91	C₂²×D₄×C₆₇	—	2	4	no	—
92	C₂²×D₄×C₆₇	—	2	1	no	—
93	C₂²×D₄×C₆₇	—	2	2	no	—
94	C₂²×D₄×C₆₇	D₄	1	2	yes	—
95	C₂²×D₄×C₆₇	D₄	1	2	yes	complemented
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
99	C₂³×C₄×C₆₇	—	2	4	no	—
100	C₂³×C₄×C₆₇	—	2	2	no	—
101	C₂³×C₄×C₆₇	D₄	1	2	yes	—
102	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
103	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
104	AGL(1,ℤ/8)×C₆₇	—	2	32	no	—
105	AGL(1,ℤ/8)×C₆₇	C₂³	1	32	yes	complemented
106	C₂×SD₁₆×C₆₇	—	2	8	no	—
107	C₂×SD₁₆×C₆₇	—	2	16	no	—
108	C₂×D₈×C₆₇	—	2	8	no	—
109	C₂×D₈×C₆₇	—	2	16	no	—
110	C₂×M₁₆×C₆₇	—	2	2	no	—
111	C₂×M₁₆×C₆₇	—	2	4	no	—
112	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
113	C₂×M₁₆×C₆₇	C₂³	1	8	yes	complemented
114	C₂²×C₈×C₆₇	—	2	2	no	—
115	#127×C₆₇	—	2	4	no	—
116	#127×C₆₇	C₂³	1	8	yes	complemented
117	#124×C₆₇	—	2	4	no	—
118	#124×C₆₇	C₂³	1	8	yes	complemented
119	#121×C₆₇	—	2	16	no	—
120	#120×C₆₇	—	2	16	no	—
121	#117×C₆₇	—	2	2	no	—
122	#117×C₆₇	C₂³	1	4	yes	complemented
123	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
126	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
127	#104×C₆₇	C₂³	1	32	yes	complemented
128	#101×C₆₇	C₂³	1	8	yes	complemented
129	#100×C₆₇	C₂³	1	8	yes	complemented
130	C₂⁴×C₆₇	—	2	4	no	—
131	C₂⁴×C₆₇	—	2	2	no	—
132	C₂⁴×C₆₇	—	2	2	no	—
133	C₂⁴×C₆₇	—	2	4	no	—
134	C₂⁴×C₆₇	—	4	2	no	—
135	C₂⁴×C₆₇	—	4	2	no	—
136	C₂⁴×C₆₇	—	8	4	no	—
137	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
138	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
139	#41×C₆₇	—	2	32	no	—
140	#41×C₆₇	—	2	64	no	—
141	#41×C₆₇	—	2	16	no	—
142	#41×C₆₇	—	2	16	no	—
143	#41×C₆₇	—	2	16	no	—
144	#41×C₆₇	—	2	32	no	—
145	#41×C₆₇	—	2	16	no	—
146	#41×C₆₇	—	2	16	no	—
147	#41×C₆₇	—	2	8	no	—
148	#41×C₆₇	—	2	8	no	—
149	#41×C₆₇	—	2	8	no	—
150	#41×C₆₇	—	2	8	no	—
151	#41×C₆₇	—	2	8	no	—
152	#41×C₆₇	—	2	8	no	—
153	#41×C₆₇	—	2	8	no	—
154	#41×C₆₇	—	2	16	no	—
155	#41×C₆₇	—	2	4	no	—
156	#41×C₆₇	—	2	8	no	—
157	#41×C₆₇	—	2	8	no	—
158	#41×C₆₇	—	2	4	no	—
159	#41×C₆₇	C₂×D₄	1	8	yes	—
160	#41×C₆₇	C₂×D₄	1	16	yes	complemented
161	#41×C₆₇	C₂⁴	1	8	yes	—
162	C₂×Q₈×C₆₇	—	2	4	no	—
163	C₂×Q₈×C₆₇	—	2	16	no	—
164	C₂×Q₈×C₆₇	—	2	16	no	—
165	C₂×Q₈×C₆₇	—	2	16	no	—
166	C₂×Q₈×C₆₇	—	2	2	no	—
167	C₂×Q₈×C₆₇	—	2	4	no	—
168	C₂×Q₈×C₆₇	—	2	2	no	—
169	C₂×Q₈×C₆₇	—	2	2	no	—
170	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
171	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
172	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	complemented
173	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
174	C₂×D₄×C₆₇	—	2	8	no	—
175	C₂×D₄×C₆₇	—	2	4	no	—
176	C₂×D₄×C₆₇	—	2	16	no	—
177	C₂×D₄×C₆₇	—	2	64	no	—
178	C₂×D₄×C₆₇	—	2	16	no	—
179	C₂×D₄×C₆₇	—	2	16	no	—
180	C₂×D₄×C₆₇	—	2	4	no	—
181	C₂×D₄×C₆₇	—	2	4	no	—
182	C₂×D₄×C₆₇	—	2	8	no	—
183	C₂×D₄×C₆₇	—	2	4	no	—
184	C₂×D₄×C₆₇	—	2	4	no	—
185	C₂×D₄×C₆₇	—	2	16	no	—
186	C₂×D₄×C₆₇	—	2	8	no	—
187	C₂×D₄×C₆₇	—	2	16	no	—
188	C₂×D₄×C₆₇	—	2	16	no	—
189	C₂×D₄×C₆₇	—	2	2	no	—
190	C₂×D₄×C₆₇	—	2	4	no	—
191	C₂×D₄×C₆₇	—	2	2	no	—
192	C₂×D₄×C₆₇	—	2	2	no	—
193	C₂×D₄×C₆₇	—	2	4	no	—
194	C₂×D₄×C₆₇	—	2	8	no	—
195	C₂×D₄×C₆₇	—	2	4	no	—
196	C₂×D₄×C₆₇	—	2	8	no	—
197	C₂×D₄×C₆₇	—	2	4	no	—
198	C₂×D₄×C₆₇	—	2	2	no	—
199	C₂×D₄×C₆₇	—	4	2	no	—
200	C₂×D₄×C₆₇	—	4	4	no	—
201	C₂×D₄×C₆₇	—	4	4	no	—
202	C₂×D₄×C₆₇	—	4	1	no	—
203	C₂×D₄×C₆₇	—	4	1	no	—
204	C₂×D₄×C₆₇	—	8	8	no	—
205	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
206	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
208	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	complemented
209	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
210	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₇	—	2	4	no	—
212	C₂²×C₄×C₆₇	—	2	8	no	—
213	C₂²×C₄×C₆₇	—	2	32	no	—
214	C₂²×C₄×C₆₇	—	2	2	no	—
215	C₂²×C₄×C₆₇	—	2	4	no	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	8	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	4	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	8	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
225	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
232	SD₁₆×C₆₇	—	2	32	no	—
233	D₈×C₆₇	—	2	32	no	—
234	M₁₆×C₆₇	—	2	4	no	—
235	M₁₆×C₆₇	—	2	8	no	—
236	M₁₆×C₆₇	C₂⁴	1	8	yes	—
237	C₂×C₈×C₆₇	—	2	4	no	—
238	C₂×C₈×C₆₇	—	2	8	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₂²⋊C₄×C₆₇	—	2	4	no	—
241	C₂²⋊C₄×C₆₇	—	2	16	no	—
242	C₄²×C₆₇	—	2	2	no	—
243	C₄²×C₆₇	C₂⁴	1	4	yes	—
244	C₂³×C₆₇	—	2	16	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	4	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	8	no	—
249	C₂³×C₆₇	—	2	4	no	—
250	C₂³×C₆₇	—	4	2	no	—
251	C₂³×C₆₇	—	4	4	no	—
252	C₂³×C₆₇	—	4	8	no	—
253	C₂³×C₆₇	—	4	2	no	—
254	C₂³×C₆₇	—	4	8	no	—
255	C₂³×C₆₇	—	4	2	no	—
256	C₂³×C₆₇	—	8	4	no	—
257	C₂³×C₆₇	—	8	8	no	—
258	C₂³×C₆₇	—	8	8	no	—
259	C₂³×C₆₇	—	8	8	no	—
260	C₂³×C₆₇	—	8	8	no	—
261	C₂³×C₆₇	#120	1	2	yes	—
262	C₂³×C₆₇	#120	1	2	yes	—
263	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
264	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
265	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
266	Q₈×C₆₇	—	2	16	no	—
267	Q₈×C₆₇	—	2	4	no	—
268	Q₈×C₆₇	—	2	4	no	—
269	Q₈×C₆₇	—	2	8	no	—
270	Q₈×C₆₇	—	2	4	no	—
271	Q₈×C₆₇	C₂²×D₄	1	8	yes	—
272	D₄×C₆₇	—	2	32	no	—
273	D₄×C₆₇	—	2	16	no	—
274	D₄×C₆₇	—	2	8	no	—
275	D₄×C₆₇	—	2	16	no	—
276	D₄×C₆₇	—	2	16	no	—
277	D₄×C₆₇	—	2	8	no	—
278	D₄×C₆₇	—	2	4	no	—
279	D₄×C₆₇	—	2	4	no	—
280	D₄×C₆₇	—	2	8	no	—
281	D₄×C₆₇	—	2	4	no	—
282	D₄×C₆₇	—	2	8	no	—
283	D₄×C₆₇	—	4	4	no	—
284	D₄×C₆₇	—	4	4	no	—
285	D₄×C₆₇	—	4	4	no	—
286	D₄×C₆₇	—	8	16	no	—
287	D₄×C₆₇	C₂²×D₄	1	8	yes	—
288	C₂×C₄×C₆₇	—	2	16	no	—
289	C₂×C₄×C₆₇	—	2	32	no	—
290	C₂×C₄×C₆₇	—	2	8	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	4	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	16	no	—
295	C₂×C₄×C₆₇	—	2	8	no	—
296	C₂×C₄×C₆₇	—	2	8	no	—
297	C₂×C₄×C₆₇	—	2	8	no	—
298	C₂×C₄×C₆₇	—	2	8	no	—
299	C₂×C₄×C₆₇	—	2	4	no	—
300	C₂×C₄×C₆₇	—	4	4	no	—
301	C₂×C₄×C₆₇	#120	1	4	yes	—
302	C₂×C₄×C₆₇	#120	1	2	yes	—
303	C₂×C₄×C₆₇	#120	1	4	yes	—
304	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
305	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
306	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
307	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
310	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
314	C₈×C₆₇	—	2	8	no	—
315	C₂²×C₆₇	—	2	2	no	—
316	C₂²×C₆₇	—	2	4	no	—
317	C₂²×C₆₇	—	2	4	no	—
318	C₂²×C₆₇	—	2	8	no	—
319	C₂²×C₆₇	—	4	2	no	—
320	C₂²×C₆₇	—	4	2	no	—
321	C₂²×C₆₇	—	4	4	no	—
322	C₂²×C₆₇	—	4	8	no	—
323	C₂²×C₆₇	—	4	4	no	—
324	C₂²×C₆₇	—	4	8	no	—
325	C₂²×C₆₇	—	4	4	no	—
326	C₂²×C₆₇	—	8	2	no	—
327	C₂²×C₆₇	—	8	8	no	—
328	C₂²×C₆₇	—	8	4	no	—
329	C₂²×C₆₇	—	8	16	no	—
330	C₂²×C₆₇	—	8	16	no	—
331	C₂²×C₆₇	—	8	4	no	—
332	C₂²×C₆₇	C₂×#120	1	4	yes	—
333	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
334	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
335	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₆₇	—	2	8	no	—
337	C₄×C₆₇	—	2	4	no	—
338	C₄×C₆₇	—	4	4	no	—
339	C₄×C₆₇	C₂×#120	1	2	yes	—
340	C₄×C₆₇	C₂×#120	1	2	yes	—
341	C₄×C₆₇	C₂×#120	1	2	yes	—
342	C₄×C₆₇	C₂³×D₄	1	2	yes	—
343	C₂×#3021	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂×C₆₇	—	2	1	no	—
345	C₂×C₆₇	—	2	1	no	—
346	C₂×C₆₇	—	2	4	no	—
347	C₂×C₆₇	—	4	4	no	—
348	C₂×C₆₇	—	4	8	no	—
349	C₂×C₆₇	—	8	4	no	—
350	C₂×C₆₇	#3021	1	2	yes	direct product factor
351	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
352	C₂×#585	C₂×C₆₇	1	1	yes	characteristic, complemented
353	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	2	yes	complemented
354	C₂×#535	C₂×C₆₇	1	1	yes	characteristic, complemented
355	#3021	C₂×C₆₇	1	16	yes	direct product factor
356	C₂×#454	C₂×C₆₇	1	4	yes	complemented
357	C₂×#453	C₂×C₆₇	1	4	yes	complemented
358	C₂×#421	C₂×C₆₇	1	2	yes	complemented
359	C₂×#413	C₂×C₆₇	1	1	yes	characteristic, complemented
360	C₆₇	C₂×#3021	1	1	yes	characteristic, direct product factor, Sylow
361	#585	—	2	4	no	—
362	#585	—	2	8	no	—
363	#585	C₂²×C₆₇	1	8	yes	complemented
364	C₂×2₋¹⁺⁴	—	2	2	no	—
365	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
366	C₂×H(5,𝔽₂)	—	2	2	no	—
367	C₂×H(5,𝔽₂)	—	2	2	no	—
368	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
369	C₂²×#41	—	2	4	no	—
370	C₂²×#41	—	2	2	no	—
371	C₂²×#41	C₂²×C₆₇	1	2	yes	—
372	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
373	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
374	C₂×AGL(1,ℤ/8)	—	2	4	no	—
375	C₂×AGL(1,ℤ/8)	—	2	8	no	—
376	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	8	yes	complemented
377	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	16	yes	complemented
378	C₂²×SD₁₆	—	2	2	no	—
379	C₂²×D₈	—	2	2	no	—
380	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
381	#535	—	2	4	no	—
382	#535	C₂²×C₆₇	1	8	yes	complemented
383	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
384	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
385	C₂×#121	—	2	2	no	—
386	C₂×#120	—	2	2	no	—
387	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
388	#454	C₂²×C₆₇	1	32	yes	complemented
389	#453	C₂²×C₆₇	1	32	yes	complemented
390	#421	C₂²×C₆₇	1	16	yes	complemented
391	C₂×#104	C₂²×C₆₇	1	8	yes	complemented
392	#413	C₂²×C₆₇	1	8	yes	complemented
393	C₂×#101	C₂²×C₆₇	1	2	yes	complemented
394	C₂×#100	C₂²×C₆₇	1	2	yes	complemented
395	C₂⁵	—	2	1	no	—
396	2₋¹⁺⁴	—	2	16	no	—
397	2₋¹⁺⁴	—	2	8	no	—
398	2₋¹⁺⁴	—	2	4	no	—
399	2₋¹⁺⁴	—	2	16	no	—
400	2₋¹⁺⁴	C₂³×C₆₇	1	8	yes	complemented
401	H(5,𝔽₂)	—	2	16	no	—
402	H(5,𝔽₂)	—	2	16	no	—
403	H(5,𝔽₂)	—	2	8	no	—
404	H(5,𝔽₂)	—	2	16	no	—
405	H(5,𝔽₂)	—	2	4	no	—
406	H(5,𝔽₂)	—	2	16	no	—
407	H(5,𝔽₂)	C₂³×C₆₇	1	8	yes	complemented
408	C₂×#41	—	2	4	no	—
409	C₂×#41	—	2	8	no	—
410	C₂×#41	—	2	4	no	—
411	C₂×#41	—	2	32	no	—
412	C₂×#41	—	2	16	no	—
413	C₂×#41	—	2	32	no	—
414	C₂×#41	—	2	4	no	—
415	C₂×#41	—	2	4	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	2	4	no	—
419	C₂×#41	—	2	16	no	—
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	2	2	no	—
422	C₂×#41	—	2	4	no	—
423	C₂×#41	—	2	4	no	—
424	C₂×#41	—	2	4	no	—
425	C₂×#41	D₄×C₆₇	1	4	yes	—
426	C₂×#41	D₄×C₆₇	1	4	yes	complemented
427	C₂×#41	D₄×C₆₇	1	8	yes	complemented
428	C₂×#41	C₂³×C₆₇	1	4	yes	—
429	C₂×#41	C₂³×C₆₇	1	8	yes	—
430	C₂×#41	C₂³×C₆₇	1	4	yes	—
431	C₂²×Q₈	—	2	2	no	—
432	C₂²×Q₈	—	2	4	no	—
433	C₂²×Q₈	D₄×C₆₇	1	2	yes	complemented
434	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
435	C₂²×D₄	—	2	8	no	—
436	C₂²×D₄	—	2	2	no	—
437	C₂²×D₄	—	2	4	no	—
438	C₂²×D₄	—	2	2	no	—
439	C₂²×D₄	—	2	4	no	—
440	C₂²×D₄	—	2	4	no	—
441	C₂²×D₄	—	2	2	no	—
442	C₂²×D₄	—	2	2	no	—
443	C₂²×D₄	—	2	4	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	2	no	—
446	C₂²×D₄	D₄×C₆₇	1	2	yes	—
447	C₂²×D₄	D₄×C₆₇	1	2	yes	complemented
448	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
449	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
450	C₂²×D₄	C₂³×C₆₇	1	4	yes	complemented
451	C₂³×C₄	—	2	4	no	—
452	C₂³×C₄	—	2	2	no	—
453	C₂³×C₄	D₄×C₆₇	1	2	yes	—
454	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
455	AGL(1,ℤ/8)	—	2	16	no	—
456	AGL(1,ℤ/8)	—	2	32	no	—
457	AGL(1,ℤ/8)	C₂³×C₆₇	1	32	yes	complemented
458	C₂×SD₁₆	—	2	8	no	—
459	C₂×SD₁₆	—	2	16	no	—
460	C₂×D₈	—	2	8	no	—
461	C₂×D₈	—	2	16	no	—
462	C₂×M₁₆	—	2	2	no	—
463	C₂×M₁₆	—	2	4	no	—
464	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
465	C₂×M₁₆	C₂³×C₆₇	1	8	yes	complemented
466	C₂²×C₈	—	2	2	no	—
467	#127	—	2	4	no	—
468	#127	C₂³×C₆₇	1	8	yes	complemented
469	#124	—	2	4	no	—
470	#124	C₂³×C₆₇	1	8	yes	complemented
471	#121	—	2	16	no	—
472	#120	—	2	16	no	—
473	#117	—	2	2	no	—
474	#117	C₂³×C₆₇	1	4	yes	complemented
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	4	no	—
478	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
479	#104	C₂³×C₆₇	1	32	yes	complemented
480	#101	C₂³×C₆₇	1	8	yes	complemented
481	#100	C₂³×C₆₇	1	8	yes	complemented
482	C₂⁴	—	2	4	no	—
483	C₂⁴	—	2	2	no	—
484	C₂⁴	—	2	2	no	—
485	C₂⁴	—	2	4	no	—
486	C₂⁴	—	4	2	no	—
487	C₂⁴	—	4	2	no	—
488	C₂⁴	—	8	4	no	—
489	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
490	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
491	#41	—	2	32	no	—
492	#41	—	2	64	no	—
493	#41	—	2	16	no	—
494	#41	—	2	16	no	—
495	#41	—	2	16	no	—
496	#41	—	2	32	no	—
497	#41	—	2	16	no	—
498	#41	—	2	16	no	—
499	#41	—	2	8	no	—
500	#41	—	2	8	no	—
501	#41	—	2	8	no	—
502	#41	—	2	8	no	—
503	#41	—	2	8	no	—
504	#41	—	2	8	no	—
505	#41	—	2	8	no	—
506	#41	—	2	16	no	—
507	#41	—	2	4	no	—
508	#41	—	2	8	no	—
509	#41	—	2	8	no	—
510	#41	—	2	4	no	—
511	#41	C₂×D₄×C₆₇	1	8	yes	—
512	#41	C₂×D₄×C₆₇	1	16	yes	complemented
513	#41	C₂⁴×C₆₇	1	8	yes	—
514	C₂×Q₈	—	2	4	no	—
515	C₂×Q₈	—	2	16	no	—
516	C₂×Q₈	—	2	16	no	—
517	C₂×Q₈	—	2	16	no	—
518	C₂×Q₈	—	2	2	no	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
523	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
524	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	complemented
525	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	16	no	—
529	C₂×D₄	—	2	64	no	—
530	C₂×D₄	—	2	16	no	—
531	C₂×D₄	—	2	16	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	8	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	16	no	—
538	C₂×D₄	—	2	8	no	—
539	C₂×D₄	—	2	16	no	—
540	C₂×D₄	—	2	16	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	8	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	4	1	no	—
552	C₂×D₄	—	4	1	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	8	8	no	—
557	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
558	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
559	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
560	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	complemented
561	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
562	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	8	no	—
565	C₂²×C₄	—	2	32	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	8	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	8	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
576	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
577	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
579	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
580	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
581	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
582	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
584	SD₁₆	—	2	32	no	—
585	D₈	—	2	32	no	—
586	M₁₆	—	2	4	no	—
587	M₁₆	—	2	8	no	—
588	M₁₆	C₂⁴×C₆₇	1	8	yes	—
589	C₂×C₈	—	2	4	no	—
590	C₂×C₈	—	2	8	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	16	no	—
594	C₄²	—	2	2	no	—
595	C₄²	C₂⁴×C₆₇	1	4	yes	—
596	C₂³	—	2	16	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	4	no	—
604	C₂³	—	4	8	no	—
605	C₂³	—	4	2	no	—
606	C₂³	—	4	8	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	8	4	no	—
609	C₂³	—	8	8	no	—
610	C₂³	—	8	8	no	—
611	C₂³	—	8	8	no	—
612	C₂³	—	8	8	no	—
613	C₂³	#120×C₆₇	1	2	yes	—
614	C₂³	#120×C₆₇	1	2	yes	—
615	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
616	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
617	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
618	Q₈	—	2	16	no	—
619	Q₈	—	2	4	no	—
620	Q₈	—	2	4	no	—
621	Q₈	—	2	8	no	—
622	Q₈	—	2	4	no	—
623	Q₈	C₂²×D₄×C₆₇	1	8	yes	—
624	D₄	—	2	32	no	—
625	D₄	—	2	16	no	—
626	D₄	—	2	8	no	—
627	D₄	—	2	16	no	—
628	D₄	—	2	16	no	—
629	D₄	—	2	8	no	—
630	D₄	—	2	4	no	—
631	D₄	—	2	4	no	—
632	D₄	—	2	8	no	—
633	D₄	—	2	4	no	—
634	D₄	—	2	8	no	—
635	D₄	—	4	4	no	—
636	D₄	—	4	4	no	—
637	D₄	—	4	4	no	—
638	D₄	—	8	16	no	—
639	D₄	C₂²×D₄×C₆₇	1	8	yes	—
640	C₂×C₄	—	2	16	no	—
641	C₂×C₄	—	2	32	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	8	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	16	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	8	no	—
650	C₂×C₄	—	2	8	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
654	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
655	C₂×C₄	#120×C₆₇	1	4	yes	—
656	C₂×C₄	#120×C₆₇	1	2	yes	—
657	C₂×C₄	#120×C₆₇	1	4	yes	—
658	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
659	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
660	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
663	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
664	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
665	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
666	C₈	—	2	8	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	8	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	8	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	4	8	no	—
677	C₂²	—	4	4	no	—
678	C₂²	—	8	2	no	—
679	C₂²	—	8	8	no	—
680	C₂²	—	8	4	no	—
681	C₂²	—	8	16	no	—
682	C₂²	—	8	16	no	—
683	C₂²	—	8	4	no	—
684	C₂²	C₂×#120×C₆₇	1	4	yes	—
685	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
686	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
687	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
688	C₄	—	2	8	no	—
689	C₄	—	2	4	no	—
690	C₄	—	4	4	no	—
691	C₄	C₂×#120×C₆₇	1	2	yes	—
692	C₄	C₂×#120×C₆₇	1	2	yes	—
693	C₄	C₂×#120×C₆₇	1	2	yes	—
694	C₄	C₂³×D₄×C₆₇	1	2	yes	—
695	C₂	—	2	1	no	—
696	C₂	—	2	1	no	—
697	C₂	—	2	4	no	—
698	C₂	—	4	4	no	—
699	C₂	—	4	8	no	—
700	C₂	—	8	4	no	—
701	C₂	C₆₇×#3021	1	2	yes	direct product factor
702	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#585×C₆₇	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
3. C₂×#535×C₆₇	C₂	semidirect
4. C₆₇×#3021	C₂	direct (N × H)
5. C₂×#454×C₆₇	C₂	semidirect
6. C₂×#453×C₆₇	C₂	semidirect
7. C₂×#421×C₆₇	C₂	semidirect
8. C₂×#413×C₆₇	C₂	semidirect
11. #585×C₆₇	C₂²	semidirect
13. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
16. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
21. C₂³×D₄×C₆₇	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
28. C₂²×M₁₆×C₆₇	C₂²	semidirect
30. #535×C₆₇	C₂²	semidirect
31. C₂×#127×C₆₇	C₂²	semidirect
32. C₂×#124×C₆₇	C₂²	semidirect
35. C₂×#117×C₆₇	C₂²	semidirect
36. #454×C₆₇	C₂²	semidirect
37. #453×C₆₇	C₂²	semidirect
38. #421×C₆₇	C₂²	semidirect
39. C₂×#104×C₆₇	C₂²	semidirect
40. #413×C₆₇	C₂²	semidirect
41. C₂×#101×C₆₇	C₂²	semidirect
42. C₂×#100×C₆₇	C₂²	semidirect
48. 2₋¹⁺⁴×C₆₇	C₂³	semidirect
55. H(5,𝔽₂)×C₆₇	C₂³	semidirect
74. C₂×#41×C₆₇	D₄	semidirect
75. C₂×#41×C₆₇	D₄	semidirect
81. C₂²×Q₈×C₆₇	D₄	semidirect
95. C₂²×D₄×C₆₇	D₄	semidirect
98. C₂²×D₄×C₆₇	C₂³	semidirect
105. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
113. C₂×M₁₆×C₆₇	C₂³	semidirect
116. #127×C₆₇	C₂³	semidirect
118. #124×C₆₇	C₂³	semidirect
122. #117×C₆₇	C₂³	semidirect
127. #104×C₆₇	C₂³	semidirect
128. #101×C₆₇	C₂³	semidirect
129. #100×C₆₇	C₂³	semidirect
160. #41×C₆₇	C₂×D₄	semidirect
172. C₂×Q₈×C₆₇	C₂×D₄	semidirect
208. C₂×D₄×C₆₇	C₂×D₄	semidirect
343. C₂×#3021	C₆₇	direct (N × H)
350. C₂×C₆₇	#3021	direct (N × H)
352. C₂×#585	C₂×C₆₇	semidirect
353. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
354. C₂×#535	C₂×C₆₇	semidirect
355. #3021	C₂×C₆₇	direct (N × H)
356. C₂×#454	C₂×C₆₇	semidirect
357. C₂×#453	C₂×C₆₇	semidirect
358. C₂×#421	C₂×C₆₇	semidirect
359. C₂×#413	C₂×C₆₇	semidirect
360. C₆₇	C₂×#3021	direct (N × H)
363. #585	C₂²×C₆₇	semidirect
365. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
368. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
373. C₂³×D₄	C₂²×C₆₇	semidirect
376. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
377. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
380. C₂²×M₁₆	C₂²×C₆₇	semidirect
382. #535	C₂²×C₆₇	semidirect
383. C₂×#127	C₂²×C₆₇	semidirect
384. C₂×#124	C₂²×C₆₇	semidirect
387. C₂×#117	C₂²×C₆₇	semidirect
388. #454	C₂²×C₆₇	semidirect
389. #453	C₂²×C₆₇	semidirect
390. #421	C₂²×C₆₇	semidirect
391. C₂×#104	C₂²×C₆₇	semidirect
392. #413	C₂²×C₆₇	semidirect
393. C₂×#101	C₂²×C₆₇	semidirect
394. C₂×#100	C₂²×C₆₇	semidirect
400. 2₋¹⁺⁴	C₂³×C₆₇	semidirect
407. H(5,𝔽₂)	C₂³×C₆₇	semidirect
426. C₂×#41	D₄×C₆₇	semidirect
427. C₂×#41	D₄×C₆₇	semidirect
433. C₂²×Q₈	D₄×C₆₇	semidirect
447. C₂²×D₄	D₄×C₆₇	semidirect
450. C₂²×D₄	C₂³×C₆₇	semidirect
457. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
465. C₂×M₁₆	C₂³×C₆₇	semidirect
468. #127	C₂³×C₆₇	semidirect
470. #124	C₂³×C₆₇	semidirect
474. #117	C₂³×C₆₇	semidirect
479. #104	C₂³×C₆₇	semidirect
480. #101	C₂³×C₆₇	semidirect
481. #100	C₂³×C₆₇	semidirect
512. #41	C₂×D₄×C₆₇	semidirect
524. C₂×Q₈	C₂×D₄×C₆₇	semidirect
560. C₂×D₄	C₂×D₄×C₆₇	semidirect
701. C₂	C₆₇×#3021	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#585×C₆₇	2
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₂×#535×C₆₇	2
C₆₇×#3021	2
C₂×#454×C₆₇	2
C₂×#453×C₆₇	2
C₂×#421×C₆₇	2
C₂×#413×C₆₇	2
C₂×#3021	67

Subgroups — C2×C67×#3021 #30739636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3021 #30739636